A raytracing inversion procedure for the extraction of the atmospheric refractivity from GNSS travel-time data

Abstract We present an inversion procedure for the extraction of atmospheric parameters from travel-time data of signals emitted by Global Navigation Satellite Systems (GNSS), such as the Global Positioning System (GPS). The procedure uses a tomographic approach, using raytracing to obtain the propagation trajectories of the electromagnetic waves. In order to allow the application of this procedure in systems processing large amounts of data, as in operational weather forecasting, we have paid attention to balance the computing time needed, the robustness of the algorithm and the accuracy of the result. We describe the inversion procedure used to extract the refractivity field. In cases cases where moderate amounts of data are available we have aimed to extract the vertical profile (i.e. we assumed that the refractivity depends only on height). We have compared this procedure with the Abel transform inversion approach, the baseline algorithm currently used for radio occultation observations, which requires the assumption that the observed field is spherically symmetric. The raytracing procedure, however, is in principle able to extract three-dimensional information (i.e. does not require the assumption that the horizontal gradients are zero), and can be used to resolve this horizontal structure from the data. However, although it is algorithmically possible, a full three-dimensional map of the field of refractive index requires massive amounts of data, which generally will not be available. In most practical operational cases a smaller, limited amount of data will be available, leading to a non-unique, and highly correlated, solution. If we used GNSS as the only source of data the result would be very poor, but in general more information is available. Instead of forcing some symmetry, we can opt to keep the correlation information and use it in the framework of an assimilation procedure. As can be seen, these are the ingredients needed to construct the “observation part” of the assimilation cost function. We can thus leave to the assimilation procedure the task of defining the symmetry properties of the refractivity field.